Someone with street experience are, in most cases, used to fighting others with the same style. Usually grappling and/or bare knuckle with a viscous twist. I doubt they see a lot of martial arts, unless they went out of their way to look for fights with strangers.

I disagree. Most street fighters have learned some martial arts moves from classes or someone else on the street and they use them to some extent in fighting. They have the experience to know what works and what is just show. If you watch a cagefight or other MMA event you might see some martial arts moves that you can point out as a certain style, but it always ends up as a grappling and punching match on the floor.
The kid I saw in Brazil used some Capoeira and Brazilian Jujitsu moves, but you could tell he wasn't a practitioner of these arts and picked these up by watching or a friend teaching him. It still ended up as a grappling and punching match on the floor in the end.